Conjugate Roots Theorem
Given a Polynomial Equation with Real Coefficients:
\[a_0+a_1x+a_2x^2+a_3x^3+\dots+a_{n-1}x^{n-1}+a_nx^n=0 \text{ where}\hspace{0.5em} a_0, a_1, a_2, a_3, \dots, a_{n-1}, a_n \in \mathbb{R}\]
If&nbsp;\(z\) is a complex root of the equation, then&nbsp;\(z^*\) is also a complex root of the equation.
Proof

Given a **Polynomial Equation** with **Real Coefficients**:

\[a_0+a_1x+a_2x^2+a_3x^3+\dots+a_{n-1}x^{n-1}+a_nx^n=0 \text{ where } a_0, a_1, a_2, a_3, \dots, a_{n-1}, a_n \in \mathbb{R}\]

If \(z\) is a complex root of the equation, then \(z^*\) is also a complex root of the equation.

Application of Conjugate Roots Theorem

Complex Numbers

International Baccalaureate Higher Level Mathematics

Complex Numbers - Application of Conjugate Roots Theorem

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